City by the Bay seeks heir to Feinstein. FAMILIAR FACES IN MAYORAL RACES

San Francisco, facing economic stagnation for the first time since World War II and losing its international status as ``gateway to the Pacific,'' is looking for a new mayor to guide it through this critical juncture. With popular two-term Mayor Dianne Feinstein prevented from running again, no fewer than 10 candidates think they are up to the task. On the eve of tomorrow's primary the outcome remains foggy. What has become clear is that no candidate is likely to get a clear majority of the votes. In that case, the top two vote-getters will go head-to-head in a Dec. 8 runoff.

Whoever takes over at City Hall will have his management skills soon put to the test. The most pressing problems here include a projected $76 million budget deficit, an increasingly expensive AIDS treatment program, a severe housing shortage, and a city deeply divided over downtown high-rise development.

``Office construction built a lot of hostility in the [residential] neighborhoods,'' says Michael S. McGill, executive director of the San Francisco Planning and Urban Research Association (SPUR). But voters' subsequent efforts to control growth helped give the city an antibusiness reputation, which is weakening the local economy, Mr. McGill says. Between 1972 and 1982, net job growth in San Francisco averaged 11,000 a year, he notes. Since then, the city has averaged a net gain of fewer than 1,000 jobs a year.

``I suspect none of the candidates really appreciates what is required to create a good business climate in San Francisco,'' says McGill.

Liberal state Assemblyman Art Agnos, who is expected to be the top vote-getter tomorrow, says he would bolster the city's Office of Economic Development. But he opposes a proposal to make San Francisco the home port of the battleship USS Missouri, although it would bring a projected 1,500 jobs to the city.

John Molinari, a 16-year veteran of the city Board of Supervisors and a supporter of letting the Navy make San Francisco the home port of the Missouri, says he would follow in the footsteps of Mayor Feinstein, his long-time ally at City Hall.

Running third in polls is Roger Boas, who served for 10 years as the city's chief administrative officer. Now an auto dealer, Mr. Boas says his business experience gives him the perspective needed to help the city's economy.

So far, the contest has had almost as many ups and downs as San Francisco has hills.

Mr. Molinari, long considered heir apparent to the mayor's seat, in recent weeks has found himself being squeezed between Mr. Agnos, to his ideological left, and Mr. Boas, to his ideological right. The early front runner, Molinari was 10 points behind Agnos in recent polls.

But Agnos is not without political baggage. He failed to report in his income-tax returns $65,000 he made on land deals arranged by his financial patron and fellow Greek-American, Angelo Tsakopoulos, a Sacramento developer. Agnos has also repeatedly missed deadlines for filing his campaign-contribution reports.

Molinari has hammered hard at Agnos's financial dealings, but his negative campaign tactics may have backfired. After Agnos and Boas began to creep up in the polls, Molinari changed his radio ads to feature a ringing endorsement from Mayor Feinstein.

Agnos and Molinari are moderate-to-liberal Democrats and tend to appeal to the same constiuency. But Agnos has taken positions on some key issues which apparently give him more appeal in the San Francisco political spectrum, which is decidedly skewed to the left. Unlike Molinari, Agnos favors a more stringent rent-control law, supports strict controls on downtown development, and opposes the proposed in-town site of a new baseball park for the San Francisco Giants.

In the most recent poll, published Friday by the San Francisco Chronicle, 39 percent favored Agnos, 25 percent Molinari, 13 percent Boas, and 5 percent other candidates. Eighteen percent were undecided.